Not surprising as the PCB appears to be identical. Which means you can use the Adafruit Arduino Library here. I suspect they are all made by Winstar, using the WS0010 or RS0010 controller, then simply re-badged.

The Midas MCOB21605G1V Data sheet can be found here, Brightness modification here

There are several HD44780 compatible LCD controllers around (e.g. KS0066, SPC780, SED1278, LC7985A), which will work fine.There are also controllers available that are compatible while providing additional features like an increased number of segment drivers for more characters or internal LCD contrast voltage generators (e.g. KS0073, KS0078, ST7036, SSD1803 and WS0010(OLED driver)).

Some of these controllers will work fine without further software changes since they just remove the need for some supporting hardware that an HD44780 based display would have used.
However, some new features require additional code and some displays won't even work without these specific new set-up instructions.

Although not currently sporting an OLED display, my LCDSmartie project below, would love the upgrade to the OLED's clarity and nano second response times!

One of many benefits to OLED, The viewing angles are as good as it gets.

Rather than the whole display being backlit, each pixel is individually lit, so black is truly black with no back light bleed, as with traditional LCD displays. Pixel response times also see a big boost!